integral transform; lattice-valued fuzzy transform; Residuated lattice; Integral kernel; Sugeno-like fuzzy integral

The integral transforms for lattice-valued functions have been introduced to generalize lower and upper fuzzy lattice-valued transforms that provide a lower and upper approximation of original functions. The paper aims to demonstrate the use of integral transforms in image processing, particularly, to filter a salt-and-pepper noise and compression and decompression of image. We consider the integral transforms defined with the help of the multiplication based Sugeno-like fuzzy integral and a fuzzy relation that serves as an integral kernel.